Mixed-gender units have been in fire fights, but some object to a wider role for female soldiers

TEL AVIV—When Maj. Or Ben Yehuda was shot in the hand by hashish smugglers in the Sinai Peninsula, she tended to a more seriously wounded male comrade while firing back at the gunmen and calling in reinforcements.

“I didn’t feel the pain at all,” she said. “I kept commanding and just trying to make sure everything was under control.”

Maj. Ben Yehuda, 27 years old, now cites that 2014 border clash in talks she gives at schools...